Freezing a saturated liquid inside a sphere

✍ Scribed by James M. Hill; Adam Kucera

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 442 KB
• Volume: 26
• Category: Article
• ISSN: 0017-9310
• DOI: 10.1016/s0017-9310(83)80083-0

✦ Synopsis

A new semi-analytical procedure is employed for the problem offreezin g a saturated liquid inside a spherical container and including the effectof radiation at the container surface. Generally moving boundary problems of this type involve a boundary layer analysis. Theapproximation scheme employed here avoids this complication and gives rise to successive estimates of the time Ie for complete solid ification of the sphere. In addition an integral formulation is adopted to independently establish bounds for Ie' The upper and lower bounds obtained are the standard order one corrected estimate of Ie and the pseudo steady-state estimate of I" respectively. Numerical values of the successive estimates for r, indicate firstly satisfactory convergence and secondly that they arc indeed consistent with the bounds independently established. Numerical values obtained for the position of the moving front are in agreement with previous results arising from both a completely numerical solution and an alternative semi-analytical solution of the problem.